1. Field
The present application relates to analog-to-digital conversion, and more specifically to analog-to-digital conversion utilizing photonic technology.
2. State of the Art
Accurate collection and processing of electromagnetic information is critical to a wide variety of applications. Present day RF and microwave sensor systems must cover many frequency bands, detect and identify a large range of signal powers, and analyze the signal information on an ever-decreasing time scale. Simultaneously achieving these attributes typically requires multiple hardware systems, stressing even the most accommodating platforms and requiring the elimination of functionality on some. The power of digital signal processing to deliver increased functionality and improved system performance has long been recognized.
The resulting preference for digital representation of signals as the format for receiver system outputs has elevated the importance of the analog-to-digital converter (ADC), which serves as the interface between the received analog signals and the digital domain. With this move to the digital domain, the ADC is and will continue to be a major bottleneck for many systems.
An ADC performs two basic functions: sampling and quantization of an incoming continuous-time signal. The quantization function is performed by rounding down to the nearest discrete level. These functions consist of the discretization of a signal in time and amplitude, respectively, as illustrated in FIGS. 1A, 1B and 1C. FIG. 1A shows a continuous-time, continuous-amplitude analog signal. FIG. 1B shows the sampling instants of the analog signal in conjunction with the analog signal itself. FIG. 1C shows the quantization levels of the analog signal in conjunction with the analog signal itself. The number of discrete amplitude levels for the ADC is most often written in terms of the number of bits required to express the levels in binary form. For example, an ADC with a resolution of 8 bits would have 28 or 256 different amplitude levels to approximate the continuous signal. The quantization function is therefore completely specified by two system parameters, the number of bits and the full-scale voltage of the ADC.
Since most ADCs take periodic measurements of the signal amplitude, the timing resolution is commonly described in terms of a uniform sample rate. The sampling rate can be specified by the frequency of sampling instants, the temporal precision of sampling instants, and the duration of the sampling window.
Timing jitter of the clock that defines the sampling instants will lead to errors in the digital representation of the sampled signal. In general, this effect can be ignored if the timing jitter is small compared with the error that is introduced by quantization. If this condition is not met, the timing jitter of the sampling clock will degrade the effective resolution of the ADC, hence the need for high-precision clock sources.
Another error that can be caused by the sampling process is signal aliasing, which is a fundamental limitation on the ability of uniform sampling to accurately represent the original continuous-time signal. The sampling theorem states that a signal of finite bandwidth can be completely reconstructed by an interpolation formula from its uniformly sampled values, so long as the sample rate is at least twice the highest frequency component of the original signal. Another way of stating this theorem is to say that for a given sample rate fs, unambiguous identification of the input signal frequency is only possible for frequencies at less than half the sample rate fs/2, known as the Nyquist frequency. After interpolation, sampled signals of higher frequency will erroneously appear to have a frequency between 0 and fs/2. Therefore, there is a tradeoff between Nyquist frequency and resolution that must be balanced for uniformly clocked ADCs. Specifically, sampling higher-frequency signals makes the timing jitter requirements increasingly difficult to satisfy, resulting in a reduced effective number of bits.